On testing proportional odds assumptions for proportional odds models

Area of Science:

• Statistics
• Biostatistics
• Ordinal Data Analysis

Background:

• Proportional odds models are widely used for ordinal response variables.
• The proportional odds assumption is critical; violations can lead to biased statistical inference.
• Existing tests for this assumption include score, Wald, and likelihood ratio (LR) tests.

Purpose of the Study:

• To review the Brant and Wolfe-Gould tests designed to evaluate the proportional odds assumption.
• To assess the performance of these tests using simulation studies and a real-world data example.
• To provide practical implementation guidance using standard statistical software.

Main Methods:

• Review of Brant's Wald-type test and Wolfe-Gould's LR-type test.
• Performance evaluation via Monte Carlo simulation studies.
• Application to a real data example.
• Provision of sample programs for SAS, SPSS, and Stata.

Main Results:

• The study evaluates the effectiveness of the Brant and Wolfe-Gould tests in detecting violations of the proportional odds assumption.
• Simulation results and the real data example demonstrate the practical utility of these tests.
• The provided sample programs facilitate the application of these diagnostic tests.

Conclusions:

• Emphasizes the necessity of assessing the proportional odds assumption in ordinal regression analyses.
• The Brant and Wolfe-Gould tests offer valuable tools for assumption checking.
• Availability of sample programs in common statistical packages enhances the accessibility of these important statistical diagnostics.